Spectroscopy and chromaticity characterization of yellow to light-blue iron-containing beryl

The chemical composition and influencing factors of the colour of 95 yellow to light blue iron-bearing beryl are studied through Electron Microprobe Analysis (EMPA), Energy-dispersive X-ray fluorescence (ED-XRF) spectroscopy, Fourier transform infrared (FTIR) spectroscopy, ultraviolet–visible (UV–vis) spectroscopy and X-Rite SP62 spectrophotometer. The intensities of the three characteristic hydroxyl stretching bands of the beryl from 3500 cm−1 to 3800 cm−1 prove they are low to medium levels of alkali bearing natural beryl. The wide absorption edge of 320 ~ 465 nm caused by the ultra-violet charge transfer from O2− to Fe3+ and the 650 nm absorption band in E//c-polarization caused by the intervalence charge transfer between Fe2+ and Fe3+ are the main factors affecting the colour of beryl. By applying CIE D65 standard light source and N9 Munsell neutral background as testing conditions, the colour parameters of 82 gem-quality beryl are tested. According to the results, iron-containing beryl colours are classified into yellow, yellowish-green, bluish-green, greenish-blue, and blue by the K-means cluster analysis method. The blue tone has a greater influence on the hue of beryl, while the yellow tone has a greater influence on the chroma. Iron content is higher in yellow and blue beryl. With the increase of iron content, the lightness of beryl decreased and the chroma increased.

Assuming that total iron is Fe 3+ , the relationships are as follows: By solving the above equations, the result shows that X Be = 0. 5079, X = 5. 7265, so the coefficient of Be is 2.9088 when iron ion is divalent. X Be = 0. 5139, X = 5. 7109 and the coefficient of Be is 2.9351 when the iron ion is trivalent. When Fe 2+ and Fe 3+ exist together in beryl, the coefficient of Be in crystal chemical formula should be 2.9088 ~ 2.9351.
The chemical formula of Icb.46 is Be 2.91~2.94 (Al 2.07~2.08 Fe 0.04 )Si 5.96 O 18 (0.01Na,0.01 K). Trace elements are generally not written into the crystal chemical formula of beryl, so the crystal chemical formula is abbreviated as Be 2.91~2.94 Al 2.07~2.08 Si 5.96 O 18 , which is very similar to the formula calculated by Taran 25 .
The crystal chemical formulas of the remaining seven samples were calculated in the same way, and the results are shown in Table 1 18 .
XRF data are used to analyze the relationship between iron content and beryl colour parameters, which will be discussed in the later paragraph.
Infrared spectral characteristics. The FTIR spectra of five beryls are given in Fig. 1. Two different kinds of water in channel show different absorption bands. Type-I water has stretching vibrations at 3698 cm −1 and (1) (3) X Be + X Si + X Al + X Mg + X Cr + X 2+ Fe · X = 11 (4) 2X Be + 4X Si + 3X Al + 2X Mg + 3X Cr + 2X 2+ Fe · X = 36 (5) X Be + X Si + X Al + X Mg + X Cr + X 3+ Fe · X = 11 (6) 2X Be + 4X Si + 3X Al + 2X Mg + 3X Cr + 3X 3+ Fe · X = 36 The absorption increases in intensity as the alkali content of the beryl rises 27 , therefore the three O-H stretching bands of 3800-3500 cm −1 can help us quickly identify the types of beryl 28,29 . According to Schmetzer and Kiefert 30 , the strong absorption band at 3694 cm −1 is designated band A. The second absorption band at 3592 cm −1 is designated band B. The absorption between bands A and B, at 3655 cm −1 is called band C. The positions of these three bands are slightly offset in the infrared spectrum of my beryl samples, their positions have been marked in Fig. 1a. The absorption intensity of these three bands of low-alkali bearing beryl is A > B > > C (Transmittance is inversely proportional to absorption intensity), and of medium-alkali bearing beryl is B > A > C. The result shows that Icb.45, Icb.47 and Icb.49 have a medium alkali content in the structural channel. However, in Icb55 and Icb.56, there are few alkali ions.
The infrared absorption bands in the range of 1300 cm −1 ~ 400 cm −1 called fingerprint area reflect the stretching and bending vibration of beryl structure 31,32 , shown in Fig. 1b. The absorptions at 1196 cm −1 ,1020 cm −1 and 955 cm −1 are related to the stretching vibrations of Si-O in E 1u 33 . The absorption band at 1196 cm -1 shifts to a higher wavenumber 1200 cm -1 . The absorption band at 1020 cm −1 increases in intensity and broadens with extent of substitution in the octahedrally site, conversely it shrinks with the increasing extent of tetrahedral substitution. The curve of this absorption band is narrow and low, and it conforms to Aurisicchio's "normal" beryl 34   www.nature.com/scientificreports/ Absorption bands around 811 cm −1 , 745 cm −1 and 682 cm −1 are mostly related to stretching vibrations of Be-O, and absorption bands at 650 and 590 cm −1 are characteristic bands for ring silicates 35 . Bands of Al-O vibrations is around 525 and 495 cm −136 . The band shift increases with the increase of octahedral distortion, especially when Al is replaced by larger divalent cations. These two bands shift slightly to low wavenumber, indicating that there are few ion substitutions et al. site 34 .
According to the 811 nm absorption position, it could be inferred that the degree of tetrahedral substitution is less than 4%. Similarly, the shift at 1196 nm indicates that the octahedral substitution of our sample is less than 5% 35 . FTIR results show that there are few tetrahedral and octahedral substitutions, so this might be the explanation for the low chroma of our beryl colour.
The weak absorption band at 2360 cm −1 correlates to the asymmetric stretching mode of CO 2 vibration which is commonly present in natural materials, but is absent in synthetic ones 37,38 . Colouration mechanism. The yellow colour of beryl comes from absorption edge between 320 and 465nm 39 . Wood and Nassau attributed the yellow colour to the ultra-violet charge transfer between Fe 3+ substituted for octahedral Al 3+ position and surrounding oxygen 3 . While Goldman and Rossman 40 believed that the Fe 3+ in the channel is responsible for the golden-yellow colour. Spinolo et al. 41 described that this absorption is caused by the colour center. Platonov et al. 42 divided the yellow beryl into heliodor and golden beryl. Heliodor refers to beryl with Fe 3+ replacing Al 3+ , while golden beryl originates from the substitution of Fe 3+ for Be 2+ . Andersson 43 gave a simple electron trap model: the electron donor is Fe 3+ at tetrahedral or octahedral position. When the crystal is heated, electrons are released from the trap and Fe 3+ is converted into Fe 2+ .
The polarized UV-vis spectra of the sample are shown in Fig. 2. The absorption edge of purple-blue area leads to the yellow colour of beryl. There is no obvious difference between E//c and E⊥c. Absorption edges exist in all beryl samples, but the absorption edges of non-yellow beryl samples are in ultraviolet region. When this absorption edge shifts from violet-blue to longer wavelengths into the blue region, yellow appears in beryl. The spectrum shows the presence of ultraviolet charge transfer below 400 nm, it shifted to the blue region, so the beryl forms a yellow appearance 44 .
The band at 620 nm in polarization E//c absorbs red light and makes beryl blue. It was firstly assigned to the Fe 2+ ions in the channel 3 and was later considered to be intervalence charge transfer between Fe 2+ substituting Al 3+ and Fe 3+ located at 6 g position 45,46 .
The absorptions at 370 nm and 425 nm correspond to the spin-forbidden transitions of Fe 3+ ( 6 A 1g → 4 T 2g and 6 A 1g → 4 E g + 4 A 1g ) in the octahedral site 47 . In the blue-tone beryl samples, these two absorptions are always present, while in the yellow-tone samples, this region is invisible covered by the absorption edge of the ultravioletblue region 48 . These two absorptions are weak and close to the ultraviolet region, so they make no contribution to beryl colour.
The strong absorption peak at 820 nm may originate from tetrahedral, octahedral or channel divalent iron 49 . It is a characteristic band of the UV-vis spectrum of beryl. In different polarization directions, this absorption has different origins. In E//c-polarization, it is attributed to Fe 2+ substituting for Al 3+ in octahedral sites. While in E⊥c-polarization, this position may indicate that the Fe 2+ in the tetrahedral site or the channel site.
The band at 956 nm only appears in the E//c-polarized UV-Vis spectra is attributed to spin-allowed 5 T 2g → 5 E g transitions of VI Fe 2+50 . It has the same origin as the absorption at 820 nm. Although these two absorbances are located outside the visible light region and have no contribution to colour, they both reveal the existence of divalent iron. Pearson correlation coefficient "r" is used to reflect the linear correlation degree of two variables X and Y, and the value of r is between -1 and 1. The larger the absolute value, the stronger the correlation. when |r|< 0.4, there is weak or no correlation; when 0.4 ≤|r|< 0.6, there is moderate correlation; when 0.6 ≤|r|< 0.8, there is high correlation; when |r|≥ 0.8, there is extremely high correlation.
By analyzing the colour data of 82 beryl, it is found that the colour coordinate a* is approximately negatively correlated with its Hue h°, as shown in Fig. 3a. The absence of the positive half axis of a* indicates that the colour of beryl is not controlled by red but by green. -b* shows the blue tone and + b* represents the yellow tone of the sample. Figure 3b and Fig. 3c shows there are 34 blue tone samples and 48 yellow -tone samples. the colour coordinate − b* is extremely high negative correlated with hue h° (Pearson's r = − 0.927, R 2 = 0.932), and + b* is extremely high negative correlated with hue h° (Pearson's r = 0.908, R 2 = 0.932).
The colour coordinate + b* is extremely high positive correlated with its chroma C* The colour coordinate + b* is extremely high positive correlated with its chroma C* (Pearson's r = 0.956, R 2 = 0.931), and the colour coordinate − b* is high negative correlated with its chroma C* (Pearson's r = − 0.770, R 2 = 0.614), indicating that the chroma of beryl is controlled by both blue and yellow tones, the influence degree of yellow is much stronger.
Compared with a*, the correlation between b* and hue h° is stronger, so the hue and chroma of beryl are mainly controlled by b*. The blue colour has a greater influence on the hue angle of beryl, while the yellow colour has a greater influence on the chroma.
The result of the colour tests shows that the hue angle of beryl ranges from 99 to 225, with an average h° of 164. The hue angle difference is about 126, which proves that the beryl samples we used in the experiment have a wide range of colour, and the experimental results are universal and representative. Because of the rich colour of iron-containing beryl, it is necessary for subsequent discussion to classify its colour. K-means cluster analysis www.nature.com/scientificreports/ is carried out with three independent colour parameters, L*, a* and b*. 3, 5, 7 and 9 are tried in turn to find the best classification scheme by comparing the number of cases and significant differences among groups. It is found that when the number of clusters is 5, the clustering effect is the best (Sig. < 0.001). The variance analysis results obtained are shown in Table 2.
Fisher discriminant function is used to test the clustering effects, the colour discriminant functions corresponding to five types of beryl are obtained as follows: The colour parameters L*, a*, b* are substituted back into five Fisher discriminant functions to discriminate, and the correct rate is 97.6%, which is in accordance with the ideal accuracy, indicating that the beryl colour classification scheme is effective.
According to the colour characteristics of each group, beryls are divided into yellow, yellowish green, bluish green, greenish blue and blue. The average values of the three parameters L*, C* and h° and the simulated colour block of the five groups of samples are shown in Table 3. The distribution of five groups in three-dimensional (7) F2 = 9.009L * − 6.185a * + 5.096b * − 409.470 (8) F2 = 9.216L * − 6.677a * + 3.923b * − 408.843  www.nature.com/scientificreports/ space is shown in Fig. 4a. Since the projection points in three-dimensional space are not intuitive enough, a chromaticity diagram is made in two-dimensional space with a* as X axis and b* as Y axis, as shown in Fig. 4b.

Relationship between iron content and colour. Iron is widely distributed in the earth's crust, and
it is also an important chromogenic ion in coloured gemstones. The valence and content of iron ions and the substitution form of iron have certain influence on the colour of beryl. The w(Fe 2 O 3 ) of 43 beryl samples was nondestructive measured by XRF, and the relationship between iron content and hue angle in beryl is shown in Fig. 5a. In yellow and blue beryl, the iron content is higher than that in green beryl. The highest Fe content appears in the samples with the highest hue angle 223.48 and chroma 17.00, and the lowest iron content is in the yellowish-green area, with a hue angle of 133.12. There is a significant negative correlation (Pearson's r = − 0.981, R 2 = 0.963) between iron content and lightness shown in Fig. 5b, the higher the iron content in beryl, the lower Figure 3. The colour analysis of beryl. (a) A negative correlation between the colour coordinate a* and its chroma C*. (b) Chromaticity coordinate − b* is highly negatively correlated with hue h°, and the colour coordinate -b* is high negative correlated with chroma C* (c) Chromaticity coordinate + b* is highly positively correlated with chromaticity C* and highly negatively correlated with hue h°.    www.nature.com/scientificreports/ its lightness. The chroma of beryl is almost proportional to iron content, but because of the low overall chroma value, there is little difference in chroma of beryl with different iron content.

Conclusion
This contribution suggested Fe is the most important chromophore in yellow to light-blue beryl. The optical spectra indicated the wide absorption edge from 300 to 465 nm caused by Fe 3+ is the origin of yellow, which does not reflect dichroism. The absorption shoulder at 650 nm in E//c-polarization is due to Fe 2+ -Fe 3+ IVCT and leading to the blue. The characteristic absorption at 820 nm may originate from tetrahedral, octahedral or channel divalent iron and the band at 956 nm only appears in the E//c-polarized direction is attributed to spin-allowed transitions of VI Fe 2+ . FTIR results show that there are few tetrahedral and octahedral substitutions, giving the explanation for the low chroma of beryl colour. The beryl colours should be divided into five groups including yellow, yellowish-green, bluish-green, greenish-blue and blue by using K-means cluster analysis. The yellow tone has much more impact on the chroma of beryl than the blue. With the help of ED-XRF, it is found that there is a certain relationship between colour and the content of iron. The yellow and blue beryl have higher iron contents than the green one. The lightness L* of beryl is negative correlated with iron content, on the contrary, the chroma C* is positive correlated with it.

Material and methods
Samples. A total of 95 natural beryl samples were collected, of which 13 were uncut crystals, the other 77 were cabochons, and 5 were platelets machined along the c axis and polished on both sides for spectral testing.
Electron microprobe analysis. EMPA-1720 was used to analyze the chemical composition of beryl, The test conditions can be described as follows: acceleration voltage: 15 kV; current: 20 mA; beam spot diameter: 5 μm. The error of EMPA depends on the content of elements. When the elements is greater than 20% wt, the relative error is less than 5%, When the element content is less than 20% wt and higher than 3%wt, the relative error is less than 10%, When the element content is less than 3% wt and higher than 1% wt, the relative error is less than 30%, when the test element content is less than 1% wt, the relative error is less than 50%.
Energy-dispersive X-ray fluorescence spectroscopy. Micro-area chemical compositions were measured using an EDX-7000 energy dispersive X-ray fluorescence spectrometer, with the following test conditions: atmosphere, oxide; a voltage of 50 kV; 108 µA. The diameter of test aperture was 3 mm.
Fourier transform infrared spectroscopy. Fourier transform infrared spectra are tested by Tensor 27 FTIR Spectrometer produced by Bruker Company of Germany. The test conditions are as follow: scanning 32 times, the wavelength range is 4000 cm -1 ~ 400 cm -1 , transmission mode, and the selected method was KBr pellets (2 mg of beryl powder mixed with 200 mg KBr).
UV-vis spectroscopy. The UV-vis spectra are tested by using UV-3600 UV-VIS spectrophotometer. The test conditions are as follows: the range of wavelength, 300 ~ 900 nm; sampling interval, 1.0 s; single scanning mode; high scanning speed.
Colourimetric analysis. The colours of beryl can be measured by X-Rite SP62 spectrophotometer in a standard illumination box with a 6504 K fluorescent lamp and the background is N9 gray level of Munsell neutral colour chips. In order to obtain accurate colour parameters, the value of each sample will be tested for three times. The test conditions are described as follows: refection method, not including the specular refection; observer view of 2°; measuring range, 400 ~ 700 nm; measuring time, 2.5 s; wavelength interval, 10 nm; voltage, 220 V; current, 50 ~ 60 Hz; measuring aperture, 4 mm.

Data availability
The dataset for this study is available from the corresponding author upon reasonable request.